Citation for published version:
Tabor, A, Thacker, M, Moseley, GL & Kording, K 2017, 'Pain: a statistical account', Plos Computational Biology,
vol. 13, no. 1, e1005142. https://doi.org/10.1371/journal.pcbi.1005142
DOI:
10.1371/journal.pcbi.1005142
Publication date:
2017
Document Version
Publisher's PDF, also known as Version of record
Link to publication
Publisher Rights
Unspecified
University of Bath
Alternative formats
If you require this document in an alternative format, please contact:
openaccess@bath.ac.uk
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners
and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
Take down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Download date: 26. Aug. 2022
REVIEW
Pain: A Statistical Account
Abby Tabor
1
, Michael A. Thacker
2,3
, G. Lorimer Moseley
3,4
, Konrad P. Ko
¨
rding
5
*
1 Centre for Pain Research, University of Bath, North East Somerset, United Kingdom, 2 Centre for Human
and Aerospace Physiological Sciences/Pain Section, Neuroimaging, Institute of Psychiatry, Kings College
London, London, United Kingdom, 3 Sansom Institute for Health Research, University of South Australia,
Adelaide, South Australia, Australia, 4 Neuroscience Research Australia, Sydney, New South Wales,
Australia, 5 Rehabilitation Institute of Chicago, Northwestern University, Chicago, Illinois, United States of
America
*
kk@northwestern.edu
Abstract
Perception is seen as a process that utilises partial and noisy information to construct a
coherent understanding of the world. Here we argue that the experience of pain is no differ-
ent; it is based on incomplete, multimodal information, which is used to estimate potential
bodily threat. We outline a Bayesian inference model, incorporating the key components of
cue combination, causal inference, and temporal integration, which highlights the statistical
problems in everyday perception. It is from this platform that we are able to review the pain
literature, providing evidence from experimental, acute, and persistent phenomena to
demonstrate the advantages of adopting a statistical account in pain. Our probabilistic
conceptualisation suggests a principles-based view of pain, explaining a broad range of
experimental and clinical findings and making testable predictions.
Introduction
In order to survive we must perceive our environment effectively, identify threats, and act to
avoid damage to our body, or, if damage occurs, we must act rapidly to promote recovery.
Pain is the fundamental experience associated with the perception of actual or potential dam-
age to one’s self [
1,2]. Despite its importance to human behaviour and to the human condition,
little is known about its computational underpinnings.
During any kind of perception, humans can only rely on previous experiences and sensory
information [
3]. The information an individual can access, however, is almost always ambigu-
ous, incomplete, or noisy [
4–6]. As such, the way we perceive the world is often conceptualized
in the perception literature as an act of statistically estimating the most likely properties of the
world on the basis of noisy information [
7,8]. In modern cognitive science, this is often formal-
ized through statistical accounts, such as Bayesian inference [
9–12], in which it is assumed that
we perceive an estimation of our sensory signals based on current information and previous
experience. This distinction between feed-forward sensory inputs and what the brain infers is
central to most current theories of perception [
13].
There are strong mathematical models for the estimation of the state of the world. These
models generally assume that each piece of information is statistically independent from the
other, conditioned on the underlying variable that is estimated. For example, in the combination
PLOS Computational Biology | DOI:10.1371/journal.pcbi.10051 42 January 12, 2017 1 / 13
a1111111111
a1111111111
a1111111111
a1111111111
a1111111111
OPEN ACCESS
Citation: Tabor A, Thacker MA, Moseley GL,
Ko¨rding KP (2017) Pain: A Statistical Account.
PLoS Comput Biol 13(1): e1005142. doi:10.1371/
journal.pcbi.1005142
Editor: Gunnar Blohm, Queen’s University,
CANADA
Published: January 12, 2017
Copyright: © 2017 Tabor et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Funding: The authors received no specific funding
for this article.
Competing Interests: The authors have declared
that no competing interests exist.
of auditory and visual information for localization (Fig 1A–1C), we may assume that each of the
cues (A,V) is observed with noise (σ
V
and σ
A
), a noisy measurement drawn from a Gaussian dis-
tribution relative to the true position (X):
A NðX; s
A
Þ; V NðX; s
V
Þ
In this case, according to Bayes rule, the optimal estimate (
^
X ) is a weighted combination of
the two:
^
X ¼
1=s
2
A
1=s
2
V
þ 1=s
2
A
V þ
1=s
2
V
1=s
2
V
þ 1=s
2
A
A
Fig 1. Cue combination in nonpain and pain perception are computationally equivalent. a–c) Simple models of cue combination involve combining two
cues: in this case, the location of a visual stimulus and the location of an auditory stimulus. The influence of each cue is dependent on the noise or precision of
the cue (probability distribution). The example shows the visual stimulus (dotted line) as more precise than the auditory cue (line-dot-dot); it, therefore, has
more influence on the estimation of the object location (solid line). d–f) Combining cues related to the potential threat to one’s body promises to provide a
better estimate of the overall threat. In this case, nociceptive information (line-dot-dot) is combined with visual information (dotted line) to produce an estimate
of threat (solid line). In this example, nociceptive information is combined with a red visual cue, increasing the overall estimation of threat as compared to the
combination of nociception and a blue cue, as demonstrated by Moseley and Arntz (2007).
doi:10.1371/journal.pcbi.1005142.g001
PLOS Computational Biology | DOI:10.1371/journal.pcbi.10051 42 January 12, 2017 2 / 13
The model simply assumes that what we see and what we hear gets combined optimally to
form an estimate of the world that considers not only different sources of information but also
how noisy they are. The same equation can be used to model a broad range of multisensory
phenomena [
12].
Pain as inference
That pain is also the result of a probability function based on incomplete or noisy information
was mooted over 20 years ago and continues to inform clinical models of pain [
14,15].
Recently, however, the idea has begun to gain traction in more theoretical and basic science
fields, instigating the formalization of pain as an inferential process [
16–19]. Relevant to this is
the substantial advance in the understanding of the physiology of nociception, the wide array
of contextual factors that have been shown to modulate pain and the increasingly tenuous rela-
tionship between pain and tissue damage that develops as pain persists [
2].
There is now a compelling body of literature to support an inferential model of pain. During the
experience of pain, just as during other perceptual experience, the brain makes inferences based on
incomplete information. Specifically, the most common trigger of pain is a somatosensory barrage
that includes, but is not limited to, activity in high threshold primary receptors (nociceptors) and
their projections. Physiologically, nociceptive input is always accompanied by—indeed, preceded
by—a wide array of non-nociceptive input triggered by other somatosensory receptors and a multi-
sensory suite of event-related information [
17]. This suite of information needs to be integrated
with prior knowledge and over time, in order to calculate the experience that would most favour-
ably serve the immediate objectives of the organism. A wealth of experimental evidence sug-
gesting that any credible indication of threat to body tissue can increase pain and any credible
indication of safety to body tissue can decrease pain [
16,20–22] clearly points to the notion that
pain results when the immediate objective of the organism is bodily protection. Importantly,
even in highly controlled laboratory experiments, away from the “real world,” pain does not
show an isomorphic relationship with the state of the tissues nor with nociceptive barrage [
15].
Understanding the generation of hugely variable pain experiences is of great importance
because pain is definitively unpleasant and disabling [
23]; a poor understanding of pain will
result in erroneous decisions about the cause of pain and, therefore, about the best course of
action. Given that persistent pain is arguably one of the world’s most burdensome health con-
ditions [
24,25], the pursuit of better models with which to make sense of pain is imperative.
Here we propose that a statistical account of pain as an inference process promises to lead to
computational insights into the mechanisms of pain and advance our understanding of the
huge variation in pain experiences between and within individuals.
For any phenomenon there can be a physiological interpretation and a normative interpre-
tation, which are not mutually exclusive [
26]. Here we start with the notion that the experience
of pain can be modelled as a perceptual experience reflecting unconscious optimal estimates
about the state of the world, which includes the body, and our best course of action within it.
We then extend this model, in line with a Bayesian inference framework, allowing the descrip-
tion of a broad range of pain phenomena. Conventionally, the investigation into such pain
experiences has been driven by dominant stimulus–response experimental models; here we
argue that the same phenomena can be advantageously reconceptualised within a statistical
model, as a special case of a generic perceptual inference process.
Concepts
This review will consider the experience of pain from a Bayesian inference perspective, specifi-
cally drawing upon examples of experimental pain, acute pain, and persistent pain. In each
PLOS Computational Biology | DOI:10.1371/journal.pcbi.10051 42 January 12, 2017 3 / 13
case, the Bayesian concepts of cue combination, causal inference, and temporal inference will
be applied to demonstrate the theoretical and practical implications of describing pain as an
inference problem.
Experimental pain: A cue combination problem
In pain research, understanding the generation of hugely variable pain experiences is of great
importance, with conventional linear stimulus–response models deemed inadequate. A broad
range of experiments has now demonstrated that the same noxious stimulus produces a hugely
variable pain response, even within the same individual, within a controlled laboratory envi-
ronment [
16,21,27–31]. Moseley and Arntz (2007) conducted an experiment to this effect,
considering the role of context and implicit expectation on the experience of pain. Pairing nox-
ious stimuli with visual cues that carried implicit meaning—a red light (semiotically linked
with heat and danger) [
32] and a blue light (semiotically linked with cool and safety)—the
authors accounted for variable pain experiences. The principle finding of this study revealed
that a noxious stimulus is perceived as hotter and more painful when it is paired with a red
visual cue than when it is paired with a blue one—for some participants, the visual cue
accounted for a doubling of pain intensity (
Fig 1D and 1E).
Furthermore, compelling evidence shows cues can evoke pain even in the absence of a nox-
ious stimulus. For example, healthy volunteers report pain during sham head stimulation
according to the level displayed on the sham stimulator’s intensity setting [
33]; clinical pain
patients report pain in response to a visual stimulus, implying their painful limb has been
touched when it has, in fact, not been touched [
34]; and, in those with movement-evoked pain
and swelling, the increase in both pain and swelling are exacerbated when the hand is made to
look swollen during movement, even though the movements themselves are identical [35].
Prompted by such findings, it has been proposed that the experience of pain reflects an
overall estimation relative to the amount of threat that is posed to the body in a particular envi-
ronment [
36,37], an estimation that requires the integration of relevant information from mul-
tisensory sources. Such a proposal demonstrates one of the core principles of Bayesian
modelling: combining relevant cues generally provides a better estimate of the variable of
interest [
28–30]. For a cue combination tutorial, see Supporting Information.
Similar to the studies conducted in pain, typical experiments on Bayesian cue combination
involve parametrically varying the reliability of two experimental variables. This could be the
visual size and the haptic size [
38] of an object. Similarly, it could involve varying the disparity
between the position of a visual cue and the position of an auditory cue [
39]. The literature
accounts for many combinations of cues and clearly shows that humans are very good at com-
bining information from multiple sources.
In accordance with Bayesian models of cue combination, typical pain experiments have
uncovered an intuitive finding that the experience of pain is relative to, but not an absolute
reflection of, nociceptive information [
15]. This contradicts the dominant stimulus–response
models of pain experimentation because it clearly demonstrates the potential potency of
explicit and implicit cue combination.
Placebo, nocebo, and causal inference
The notion that perceptual experience depends on the integration of information is a simplifi-
cation of the real world readily exposed in experimental settings. In reality, we are constantly
required to infer whether cues, from multiple sources including memories, expectations, and
beliefs, belong together or whether they should be treated as separate. The problem of inferring
whether cues belong together can be observed in the experience of pain. Being able to
PLOS Computational Biology | DOI:10.1371/journal.pcbi.10051 42 January 12, 2017 4 / 13